Uses of Effective Field Theory in Lattice QCD

TL;DR

This paper discusses how effective field theories are essential tools in lattice QCD calculations, helping to control uncertainties and improve the accuracy of non-perturbative QCD results across various physical applications.

Contribution

It provides a comprehensive review of the application of different effective field theories in lattice QCD to manage systematic uncertainties and enhance result reliability.

Findings

Effective field theories help control lattice spacing effects.

Chiral perturbation theory aids in reaching the chiral limit.

Field theory of hadrons improves finite volume correction estimates.

Abstract

Several physical problems in particle physics, nuclear physics, and astrophysics require information from non-perturbative QCD to gain a full understanding. In some cases the most reliable technique for quantitative results is to carry out large-scale numerical calculations in lattice gauge theory. As in any numerical technique, there are several sources of uncertainty. This chapter explains how effective field theories are used to keep them under control and, then, obtain a sensible error bar. After a short survey of the numerical technique, we explain why effective field theories are necessary and useful. Then four important cases are reviewed: Symanzik's effective field theory of lattice spacing effects; heavy-quark effective theory as a tool for controlling discretization effects of heavy quarks; chiral perturbation theory as a tool for reaching the chiral limit; and a general field theory of hadrons for deriving finite volume corrections.